F. Romaniello

The Pairing-Hamiltonian property in Cartesian products of graphs

Let $G$ be a simple graph of even order at least four, and let $K_G$ denote the complete graph on $V(G)$. A perfect matching of $K_G$ is called a pairing of $G$. The graph $G$ has the Pairing-Hamiltonian property, or PH-property, if every pairing $M$ of $G$ admits a perfect matching $N\subseteq E(G)$, disjoint from $M$...